Yes, you have the right to speak out, hand out flyers and petitions, and wear expressive clothing — as long as you don't disrupt the functioning of the school or violate school policies that don't hinge on the message expressed.
What counts as "disruptive" will vary by context, but a school disagreeing with your position or thinking your speech is controversial or in "bad taste" is not enough to qualify.
Courts have upheld students' rights to wear things like an anti-war armband, an armband opposing the right to get an abortion, and a shirt supporting the LGBTQ community. Schools can have rules that have nothing to do with the message expressed, like dress code. So, for example, a school can prohibit you from wearing hats— because that rule is not based on what the hat says— but it can't prohibit you from wearing only pink pussycat hats or pro-NRA hats. Outside of school, you can enjoy essentially the same rights to protest and speak out as anyone else. This means you're likely to be most protected if you organize, protest, and advocate for your view off campus and outside of school hours. You have the right to speak your mind on social media, and your school cannot punish you for content you post off campus and outside of school hours that does not relate to school.